Article
Multidisciplinary Sciences
Jianxiang Yang, Jianbin Xiong, Jian Cen, Wei He
Summary: This paper focuses on the finite-time generalized synchronization problem of non-identical fractional order chaotic (or hyper-chaotic) systems by designing an adaptive sliding mode controller. The effects of disturbances and model uncertainties are taken into account. The proposed approach is validated through numerical simulations, and a novel speech cryptosystem is proposed based on the generalized finite-time synchronization criterion.
Article
Mathematics, Applied
Hui Fu, Yonggui Kao
Summary: This paper proposes two adaptive sliding mode control (ASMC) strategies for achieving finite-time synchronization of uncertain general fractional unified chaotic systems (UGFUCSs) in the presence of uncertainty and external disturbance. The general fractional unified chaotic system (GFUCS) is first developed, which can be transitioned from the general Lorenz system to the general Chen system using a general kernel function. Two ASMC methods are then employed to achieve finite-time synchronization of UGFUCSs, where the system states reach the sliding surfaces within a finite time. The first ASMC approach uses three sliding mode controllers for synchronization between chaotic systems, while the second ASMC method only requires one sliding mode controller. The effectiveness of the proposed ASMC approaches is verified through numerical simulations.
Article
Engineering, Mechanical
A. A. Kuz'menko
Summary: This article presents a method for constructing robust synchronization laws using a synergy-cybernetic approach, which shows good performance in terms of parametric perturbations and system stability.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Electrical & Electronic
Xin Meng, Zhengtian Wu, Cunchen Gao, Baoping Jiang, Hamid Reza Karimi
Summary: This brief introduces a method for addressing the problem of finite-time projective synchronization of variable-order fractional chaotic systems using sliding mode control. The method involves designing novel sliding surfaces and control strategies to ensure system stability and obtaining a criterion for finite-time stability.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Acoustics
Samaneh Payandeh Najafabadi, Mahnaz Hashemi
Summary: This article investigates the problem of adaptive sliding synchronization for Duffing-Holmes fractional-order chaotic systems in the presence of dead-zone, disturbance, and uncertainty. The proposed adaptive sliding mode controller guarantees the asymptotic stability of the system despite the presence of the dead-zone and uncertainty. Simulation results show the validity and effectiveness of the proposed controller for synchronization of Duffing-Holmes fractional-order chaotic systems perturbed by the dead-zone, disturbance, and uncertainty.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Xia Wang, Bin Xu, Peng Shi, Shuai Li
Summary: This paper investigates the synchronization control problem for a class of fractional-order chaotic systems with unknown dynamics and disturbance. A new design scheme is proposed to achieve higher synchronization accuracy and better estimation performance. The controller is constructed using neural approximation and disturbance estimation, and the simulation results demonstrate the effectiveness of the proposed approach.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Zahra Rasooli Berardehi, Chongqi Zhang, Mostafa Taheri, Majid Roohi, Mohammad Hassan Khooban
Summary: This paper introduces a dynamic-free T-S fuzzy sliding mode control method for synchronizing different chaotic fractional-order systems in the presence of input saturation. Using a new definition of fractional calculus and the fractional version of the Lyapunov stability theorem and linear matrix inequality concept, the proposed controller is able to suppress and synchronize the undesired behavior of the fractional-order chaotic systems without any chattering phenomenon. An example of synchronization of complex power grid systems is provided to illustrate the theoretical result of the paper in real-world applications.
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
(2023)
Article
Computer Science, Information Systems
Mostafa Taheri, Chongqi Zhang, Zahra Rasooli Berardehi, Yucheng Chen, Majid Roohi
Summary: The study introduces a chattering-free fractional-integral-based sliding mode control method for synchronizing different chaotic fractional-order systems and avoiding undesired chattering phenomenon. By utilizing the boundedness property of the fractional-order chaotic system, a new control method is designed and validated in electrical systems and secure communications to demonstrate its effectiveness.
MULTIMEDIA TOOLS AND APPLICATIONS
(2022)
Article
Nanoscience & Nanotechnology
Lu Han, Lili Zhang, Yong Chen
Summary: An observer-based backstepping strategy is proposed for fractional-order chaotic systems. Disturbance observer and state observer are constructed to estimate uncertain disturbances and unmeasurable states, respectively. A fractional-order command filter is used to reduce computational burden. A coupling backstepping controller is developed to ensure the convergence of tracking error and the boundedness of closed-loop signals.
Article
Mathematics, Applied
Hanlin Dong, Jinde Cao, Heng Liu
Summary: In this paper, an observer-based event-triggered adaptive fuzzy backstepping synchronization control method is proposed for a class of uncertain fractional order chaotic systems. Fuzzy logic systems are used to estimate unknown functions and a fractional order command filter is designed to avoid complexity problems. An effective error compensation mechanism is devised to reduce filter error and improve synchronization accuracy. The designed controller ensures convergence of the synchronization error and avoids Zeno behavior, as demonstrated through numerical simulations.
Article
Mathematics, Interdisciplinary Applications
Fei Qi, Jianfeng Qu, Yi Chai, Liping Chen, Antonio M. Lopes
Summary: This paper investigates the synchronization of incommensurate fractional-order (FO) chaotic systems and proposes a sufficient condition for achieving synchronization using linear matrix inequalities (LMIs). The effectiveness and feasibility of the method are demonstrated through examples involving two typical FO chaotic systems.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Mohammadreza Askari Sepestanaki, Mohammad Soofi, Mojtaba Hadi Barhaghtalab, Hamidreza Bahmani, Saleh Mobayen, Abolfazl Jalilvand
Summary: This study proposes an adaptive continuous barrier function as a fractional-order control system to stabilize chaotic systems with unknown uncertainties using the terminal sliding mode control technique with chattering-free property. The greater flexibility of the fractional-order controller compared to the integer-order controller is the main reason for its usage. Applying an adaptive approach and Lyapunov's stability theory, the study presents an adaptive continuous barrier fractional-order chattering-free finite-time controller for chaotic systems with unknown uncertainties and external disturbances. The suggested controller can effectively stabilize the chaotic system with a continuous and smooth control law, even without knowledge of the system boundaries, and in the presence of unknown disturbances caused by model uncertainties. MATLAB simulation results confirm the high efficiency of the proposed control technique in controlling chaotic systems with unknown perturbations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Acoustics
Abdullah Gokyildirim, Haris Calgan, Metin Demirtas
Summary: In this study, the chaotic behavior of a 4D memristive Chen system is investigated by taking the order of the system as fractional. The nonlinear behavior of the system is observed numerically by comparing the fractional-order bifurcation diagrams and Lyapunov Exponents Spectra with 2D phase portraits. Two different fractional orders are determined where the system shows chaotic behavior. Furthermore, a single state fractional-order sliding mode controller (FOSMC) is designed to maintain the states of the system on the equilibrium points.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Engineering, Aerospace
Wenjie Qing, Binfeng Pan, Yueyang Hou, Shan Lu, Wenjing Zhang
Summary: In this study, a novel fractional-order sliding mode-based control method was developed for a class of nonautonomous nonlinear systems, using a fractional stability theorem and a fractional-order sliding surface. The applicability and efficiency of the proposed method were demonstrated through simulation results.
Article
Computer Science, Information Systems
Abdul-Wahid A. Saif, Khaled Bin Gaufan, Sami El-Ferik, Mujahed Al-Dhaifallah
Summary: This research proposes the implementation of two advanced controllers with integer and fractional order quadrotor systems to enhance control performance, robustness, and accuracy. MATLAB simulation studies verify the effectiveness of the approach, showing that the fractional order quadrotor system outperforms the traditional integer order system. The study highlights the potential of fractional order modeling and control techniques in improving quadrotor system performance, with implications for modern control engineering.
Article
Mathematics, Interdisciplinary Applications
Juan Wu, Yong Xu, Shaojuan Ma
CHAOS SOLITONS & FRACTALS
(2019)
Article
Mathematics, Interdisciplinary Applications
Di Liu, Yong Xu
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2019)
Article
Engineering, Mechanical
Xiaole Yue, Yanyan Wang, Qun Han, Yong Xu, Wei Xu
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2019)
Article
Engineering, Mechanical
Di Liu, Yanru Wu, Yong Xu, Jing Li
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2019)
Article
Mathematics, Applied
Bin Pei, Yong Xu, Jiang-Lun Wu
APPLIED MATHEMATICS LETTERS
(2020)
Article
Mathematics, Applied
Yong Xu, Hao Zhang, Yongge Li, Kuang Zhou, Qi Liu, Juergen Kurths
Article
Mathematics, Applied
Qi Liu, Yong Xu, Juergen Kurths
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2020)
Article
Physics, Multidisciplinary
Yongge Li, Ruoxing Mei, Yong Xu, Juergen Kurths, Jinqiao Duan, Ralf Metzler
NEW JOURNAL OF PHYSICS
(2020)
Article
Engineering, Multidisciplinary
RuiLan Tian, ZhiJie Zhao, Yong Xu
Summary: This study introduces a variable scale-convex-peak method for identifying the frequency of weak harmonic signals. By finding optimal identification coefficients and utilizing the stochastic Melnikov method, the method is able to identify the frequency while ensuring dynamic behavior transition persistence. Through analyzing the bifurcation diagram and introducing reversible scaling transformation, the feasibility of frequency detection in engineering is validated.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Ruoxing Mei, Yong Xu, Yongge Li, Juergen Kurths
CHAOS SOLITONS & FRACTALS
(2020)
Article
Engineering, Mechanical
Jinzhong Ma, Yong Xu, Yongge Li, Ruilan Tian, Guanrong Chen, Juergen Kurths
NONLINEAR DYNAMICS
(2020)
Article
Physics, Multidisciplinary
Wantao Jia, Yong Xu, Dongxi Li, Rongchun Hu
Summary: This paper investigates the statistical responses of two-special prey-predator type ecosystem models excited by combined Gaussian and Poisson white noise using the stochastic averaging method. The method effectively computes the statistical characteristics of population densities in ecosystems, including stationary probability density functions and moments.
Article
Mathematics
Seyfeddine Moualkia, Yong Xu
Summary: This paper discusses the existence and uniqueness of solutions to fractional stochastic differential equations with variable order, providing new sufficient conditions for uniqueness.
Article
Chemistry, Multidisciplinary
Rong Guo, Qi Liu, Junlin Li, Yong Xu
Summary: This study analytically explored the influences of random excitation on a shape memory alloy (SMA) oscillator, introducing a stochastic SMA model and verifying theoretical analysis through numerical simulations. The research found that random excitation significantly impacts the dynamics of the SMA model.
APPLIED SCIENCES-BASEL
(2021)
Article
Mathematics, Applied
Bin Pei, Yong Xu, Yuzhen Bai
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2020)
